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<title>Indexing tensors</title>

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<h1 class="title toc-ignore">Indexing tensors</h1>



<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(torch)</span></code></pre></div>
<p>In this article we describe the indexing operator for torch tensors and how it compares to the R indexing operator for arrays.</p>
<p>Torch’s indexing semantics are closer to numpy’s semantics than R’s. You will find a lot of similarities between this article and the <code>numpy</code> indexing article available <a href="https://docs.scipy.org/doc/numpy-1.10.0/user/basics.indexing.html">here</a>.</p>
<div id="single-element-indexing" class="section level2">
<h2>Single element indexing</h2>
<p>Single element indexing for a 1-D tensors works mostly as expected. Like R, it is 1-based. Unlike R though, it accepts negative indices for indexing from the end of the array. (In R, negative indices are used to remove elements.)</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">torch_tensor</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">10</span>)</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">1</span>]</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; 1</span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{} ]</span></span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a>x[<span class="sc">-</span><span class="dv">1</span>]</span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; 10</span></span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{} ]</span></span></code></pre></div>
<p>You can also subset matrices and higher dimensions arrays using the same syntax:</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>x <span class="ot">&lt;-</span> x<span class="sc">$</span><span class="fu">reshape</span>(<span class="at">shape =</span> <span class="fu">c</span>(<span class="dv">2</span>,<span class="dv">5</span>))</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>x</span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   1   2   3   4   5</span></span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   6   7   8   9  10</span></span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{2,5} ]</span></span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">1</span>,<span class="dv">3</span>]</span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; 3</span></span>
<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{} ]</span></span>
<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">1</span>,<span class="sc">-</span><span class="dv">1</span>]</span>
<span id="cb3-12"><a href="#cb3-12" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb3-13"><a href="#cb3-13" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; 5</span></span>
<span id="cb3-14"><a href="#cb3-14" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{} ]</span></span></code></pre></div>
<p>Note that if one indexes a multidimensional tensor with fewer indices than dimensions, one gets an error, unlike in R that would flatten the array. For example:</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">1</span>]</span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  1</span></span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  2</span></span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  3</span></span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  4</span></span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  5</span></span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{5} ]</span></span></code></pre></div>
</div>
<div id="slicing-and-striding" class="section level2">
<h2>Slicing and striding</h2>
<p>It is possible to slice and stride arrays to extract sub-arrays of the same number of dimensions, but of different sizes than the original. This is best illustrated by a few examples:</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">torch_tensor</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">10</span>)</span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>x</span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   1</span></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   2</span></span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   3</span></span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   4</span></span>
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   5</span></span>
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   6</span></span>
<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   7</span></span>
<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   8</span></span>
<span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   9</span></span>
<span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  10</span></span>
<span id="cb5-14"><a href="#cb5-14" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{10} ]</span></span>
<span id="cb5-15"><a href="#cb5-15" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">2</span><span class="sc">:</span><span class="dv">5</span>]</span>
<span id="cb5-16"><a href="#cb5-16" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb5-17"><a href="#cb5-17" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  2</span></span>
<span id="cb5-18"><a href="#cb5-18" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  3</span></span>
<span id="cb5-19"><a href="#cb5-19" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  4</span></span>
<span id="cb5-20"><a href="#cb5-20" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  5</span></span>
<span id="cb5-21"><a href="#cb5-21" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{4} ]</span></span>
<span id="cb5-22"><a href="#cb5-22" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">1</span><span class="sc">:</span>(<span class="sc">-</span><span class="dv">7</span>)]</span>
<span id="cb5-23"><a href="#cb5-23" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb5-24"><a href="#cb5-24" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  1</span></span>
<span id="cb5-25"><a href="#cb5-25" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  2</span></span>
<span id="cb5-26"><a href="#cb5-26" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  3</span></span>
<span id="cb5-27"><a href="#cb5-27" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  4</span></span>
<span id="cb5-28"><a href="#cb5-28" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{4} ]</span></span></code></pre></div>
<p>You can also use the <code>1:10:2</code> syntax which means: In the range from 1 to 10, take every second item. For example:</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">1</span><span class="sc">:</span><span class="dv">5</span><span class="sc">:</span><span class="dv">2</span>]</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  1</span></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  3</span></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  5</span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{3} ]</span></span></code></pre></div>
<p>Another special syntax is the <code>N</code>, meaning the size of the specified dimension.</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">5</span><span class="sc">:</span>N]</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   5</span></span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   6</span></span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   7</span></span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   8</span></span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   9</span></span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  10</span></span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{6} ]</span></span></code></pre></div>
</div>
<div id="getting-the-complete-dimension" class="section level2">
<h2>Getting the complete dimension</h2>
<p>Like in R, you can take all elements in a dimension by leaving an index empty.</p>
<p>Consider a matrix:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">torch_randn</span>(<span class="dv">2</span>, <span class="dv">3</span>)</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>x</span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  1.6263  2.1773 -1.2879</span></span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; -1.3563 -1.2245 -1.6768</span></span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPUFloatType{2,3} ]</span></span></code></pre></div>
<p>The following syntax will give you the first row:</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">1</span>,]</span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  1.6263</span></span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  2.1773</span></span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; -1.2879</span></span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPUFloatType{3} ]</span></span></code></pre></div>
<p>And this would give you the first 2 columns:</p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>x[,<span class="dv">1</span><span class="sc">:</span><span class="dv">2</span>]</span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  1.6263  2.1773</span></span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; -1.3563 -1.2245</span></span>
<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPUFloatType{2,2} ]</span></span></code></pre></div>
</div>
<div id="dropping-dimensions" class="section level2">
<h2>Dropping dimensions</h2>
<p>By default, when indexing by a single integer, this dimension will be dropped to avoid the singleton dimension:</p>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">torch_randn</span>(<span class="dv">2</span>, <span class="dv">3</span>)</span>
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">1</span>,]<span class="sc">$</span>shape</span>
<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [1] 3</span></span></code></pre></div>
<p>You can optionally use the <code>drop = FALSE</code> argument to avoid dropping the dimension.</p>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>x[<span class="dv">1</span>,,drop <span class="ot">=</span> <span class="cn">FALSE</span>]<span class="sc">$</span>shape</span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [1] 1 3</span></span></code></pre></div>
</div>
<div id="adding-a-new-dimension" class="section level2">
<h2>Adding a new dimension</h2>
<p>It’s possible to add a new dimension to a tensor using index-like syntax:</p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">torch_tensor</span>(<span class="fu">c</span>(<span class="dv">10</span>))</span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>x<span class="sc">$</span>shape</span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [1] 1</span></span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a>x[, newaxis]<span class="sc">$</span>shape</span>
<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [1] 1 1</span></span>
<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a>x[, newaxis, newaxis]<span class="sc">$</span>shape</span>
<span id="cb13-7"><a href="#cb13-7" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [1] 1 1 1</span></span></code></pre></div>
<p>You can also use <code>NULL</code> instead of <code>newaxis</code>:</p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>x[,<span class="cn">NULL</span>]<span class="sc">$</span>shape</span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [1] 1 1</span></span></code></pre></div>
</div>
<div id="dealing-with-variable-number-of-indices" class="section level2">
<h2>Dealing with variable number of indices</h2>
<p>Sometimes we don’t know how many dimensions a tensor has, but we do know what to do with the last available dimension, or the first one. To subsume all others, we can use <code>..</code>:</p>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>z <span class="ot">&lt;-</span> <span class="fu">torch_tensor</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">125</span>)<span class="sc">$</span><span class="fu">reshape</span>(<span class="fu">c</span>(<span class="dv">5</span>,<span class="dv">5</span>,<span class="dv">5</span>))</span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>z[<span class="dv">1</span>,..]</span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   1   2   3   4   5</span></span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   6   7   8   9  10</span></span>
<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  11  12  13  14  15</span></span>
<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  16  17  18  19  20</span></span>
<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  21  22  23  24  25</span></span>
<span id="cb15-9"><a href="#cb15-9" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{5,5} ]</span></span>
<span id="cb15-10"><a href="#cb15-10" aria-hidden="true" tabindex="-1"></a>z[..,<span class="dv">1</span>]</span>
<span id="cb15-11"><a href="#cb15-11" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; torch_tensor</span></span>
<span id="cb15-12"><a href="#cb15-12" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;    1    6   11   16   21</span></span>
<span id="cb15-13"><a href="#cb15-13" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   26   31   36   41   46</span></span>
<span id="cb15-14"><a href="#cb15-14" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   51   56   61   66   71</span></span>
<span id="cb15-15"><a href="#cb15-15" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   76   81   86   91   96</span></span>
<span id="cb15-16"><a href="#cb15-16" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;  101  106  111  116  121</span></span>
<span id="cb15-17"><a href="#cb15-17" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; [ CPULongType{5,5} ]</span></span></code></pre></div>
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